泽塔转换器:基于卡里托诺夫多项式的间隔缩小顺序建模
1Department of Electrical Engineering, National Institute of Technology, Jamshedpur, 831014, Jharkhand, India.
ISA transactions
|April 29, 2025
概括
这项研究提出了一种创新的方法,用于创建简化,精确的模型Zeta转换器. 这项研究有效地减少了模型的复杂性,同时保持了基本的性能特征.
科学领域:
- 电气工程 电气工程
- 控制系统理论 控制系统理论
- 计算数学 计算数学 计算数学
背景情况:
- 泽塔转换器在动力电子中至关重要,但往往需要复杂的模型.
- 减少模型订单对于高效的分析和控制器设计至关重要.
- 现有的方法可能无法充分处理转换器参数间隔的不确定性.
研究的目的:
- 为了开发一个连续间隔的减少顺序模型 (ROM) 的第四阶Zeta转换器.
- 使用卡里托诺夫多项式和间隔算术来实现强大的模型缩小.
- 为了验证拟议的ROM的准确性和性能与更高阶模型相比.
主要方法:
- 使用区间算术获得第四阶连续区间转移函数.
- 通过Kharitonov多项式,将模型顺序减少到第一,第二和第三个顺序.
- 导出分母的Kharitonov多项式,并构建一个Routh表.
- 匹配时间时刻 (TiMo) 和马尔科夫参数 (MaPa) 来确定ROM计数器.
主要成果:
- 成功生成了Zeta转换器的第一个,第二个和第三个顺序间隔的减少顺序模型.
- 通过与现有模型进行比较,证明了拟议方法的有效性.
- 使用步骤/冲动响应和波德/尼科尔斯对间隔界限的图表验证了性能.
- 用于比较分析的表格化时间域规范 (TDS) 和性能错误标准 (PEC).
结论:
- 提出的基于Kharitonov多项式的方法有效地减少了Zeta转换器模型的顺序.
- 降低阶模型保持了高精度和性能,与高阶模型相美.
- 这种方法提供了一种计算效率高的方法来分析功率电子中的间隔系统.
相关概念视频
01:24Difference Equation Solution using z-Transform
207
The z-transform is a powerful tool for analyzing practical discrete-time systems, often represented by linear difference equations. Solving a higher-order difference equation requires knowledge of the input signal and the initial conditions up to one term less than the order of the equation.
The z-transform facilitates handling delayed signals by shifting the signal in the z-domain, which corresponds to delaying the signal in the time domain, and advancing signals by similarly shifting in the...
The z-transform facilitates handling delayed signals by shifting the signal in the z-domain, which corresponds to delaying the signal in the time domain, and advancing signals by similarly shifting in the...
207
01:20Inverse z-Transform by Partial Fraction Expansion
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The inverse z-transform is a crucial technique for converting a function from its z-domain representation back to the time domain. One effective method for finding the inverse z-transform is the Partial Fraction Method, which involves decomposing a function into simpler fractions with distinct coefficients. These fractions correspond to known z-transform pairs, facilitating the inverse transformation process.
To begin the process, the poles of the function are identified and the function is...
To begin the process, the poles of the function are identified and the function is...
235
01:26Definition of z-Transform
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The z-transform is a powerful mathematical tool used in the analysis of discrete-time signals and systems. It is an essential analytical tool, analogous to the Laplace transform used in continuous-time systems. It plays a crucial role in the analysis of signals and systems, complementing the discrete-time Fourier transform. Both the z-transform and the Laplace transform convert differential or difference equations into algebraic equations, simplifying the process of solving complex problems.
227
01:19Routh-Hurwitz Criterion II
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In the application of the Routh-Hurwitz criterion, two specific scenarios can arise that complicate stability analysis.
The first scenario occurs when a singular zero appears in the first column of the Routh table. This situation creates a division by zero issues. To resolve this, a small positive or negative number, denoted as epsilon (∈), is substituted for the zero. The stability analysis proceeds by assuming a sign for ∈. If ∈ is positive, any sign change in the first...
The first scenario occurs when a singular zero appears in the first column of the Routh table. This situation creates a division by zero issues. To resolve this, a small positive or negative number, denoted as epsilon (∈), is substituted for the zero. The stability analysis proceeds by assuming a sign for ∈. If ∈ is positive, any sign change in the first...
156
01:17Properties of the z-Transform I
130
The z-transform is a fundamental tool in digital signal processing, enabling the analysis of discrete-time systems through its various properties. It is an invaluable tool for analyzing discrete-time systems, offering a range of properties that simplify complex signal manipulations. One fundamental property is linearity. For any two discrete-time signals, the z-transform of their linear combination equals the same linear combination of their individual z-transforms. This property is essential...
130
01:25Transformers with Off-Nominal Turns Ratios
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In scenarios involving parallel transformers with disparate ratings, developing per-unit models requires accommodating off-nominal turns ratios. This situation arises when the selected base voltages are not proportional to the transformer’s voltage ratings. Consider a transformer where the rated voltages are related by the term a. If the chosen voltage bases satisfy a relationship involving term b, term c is defined as the ratio of these bases. This ratio is then substituted into the...
122